5 inches : 2 feet. If the gym is 170 inches wide in the drawing, how wide is the actual gym?

Yes, we can fit four (2 in x 2 in x 2 in) cubes inside a sphere with a diameter of 4 inches.

Given are four 2 in x 2 in x 2 in cubes and a sphere with a diameter of 4 inches.

The cubes can fit if -

V{cubes} < V{sphere}

{4 x a³} < {4/3πr³}

{4 x 8} < {4/3 x 3.14 x 8}

32 < 33.49

which is true

Therefore, Yes, we can fit four (2 in x 2 in x 2 in) cubes inside a sphere with a diameter of 4 inches.

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Check the picture below.

so hmmm let's firstly convert the angles to degrees only.

so there are 60 minutes in 1 degree, so 10' is really 10/60 = 1/6 of a degree, so 112°10' is really just 112 and 1/6 degrees.

15°20' is just well, 20/60 = 1/3, so that converted to degrees only will be 15 and 1/3 degrees.

now, a triangle has a total of 180° interior angles, so let's get the angle A

[tex]\stackrel{mixed}{112\frac{1}{6}}\implies \cfrac{112\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{673}{6}} ~\hfill \stackrel{mixed}{15\frac{1}{3}} \implies \cfrac{15\cdot 3+1}{3} \implies \stackrel{improper}{\cfrac{46}{3}} \\\\[-0.35em] ~\dotfill\\\\ 180-\cfrac{673}{6}-\cfrac{46}{3}\implies \cfrac{105}{2}\implies 52.5^o\impliedby \measuredangle A \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(C)}{c}=\cfrac{\sin(A)}{a}\implies \cfrac{\sin(\frac{46}{3}^o)}{c}=\cfrac{\sin(52.5^o)}{354}\implies \cfrac{\sin(\frac{46}{3}^o)}{\sin(52.5^o)}=\cfrac{c}{354} \\\\\\ \cfrac{354\sin(\frac{46}{3}^o)}{\sin(52.5^o)}=c\implies 117.99^o\approx c=AB[/tex]

Make sure your calculator is in Degree mode.

Answer:

The cost of the car with sales tax would be $23,406.38.

Step-by-step explanation:

You can calculate this by adding the sales tax to the cost of the car:

$21,500 * 8.25% = $1,786.25

$21,500 + $1,786.25 = $23,286.25

The answers to each part is mentioned above.

Given is the term -

Accompanying percentiles

The kth percentile of a set of data is a value such that {k} percent of the observations are less than or equal to the value.

10% of​ 3- to​ 5-month-old males have a head circumference that is 41.0 cm or less.

90​% of​ 2-year-old females have a waist circumference that is 52.7 cm or less.

At each​ percentile, the heights generally decrease as the age increases. Assuming that an adult male does not grow after age​ 20, the percentiles imply that adults born in 1990 are generally taller than adults who were born in 1950.

Therefore, the answers to each part is mentioned above.

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The required average mark for a one-hour exam is given as 81, as per the given condition.  

The average of the values is the ratio of the total sum of values to the number of values.

To find the student's grade, we need to calculate the average of all the exams. The total number of 1-hour exams is 4 + 2 = 6, so the total number of hours of exams is 6 * 1 hour = 6 hours.

First, we find the average of the four 1-hour exams: (63 + 78 + 95 + 90) ÷ 4 = 316 ÷ 4 = 79.

Next, we add the final exam grade, which counts as two 1-hour exams, to find the total number of exam points: 79 * 4 + 85 * 2 = 316 + 170 = 486.

Finally, we divide the total number of points by the total number of hours of exams to find the average exam grade: 486 ÷ 6 = 81.

So, the student's average exam grade is 81.

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Answer:

c(3a) = 2(3a)^2 - 4(3a) + 3 = 18a^2 - 12a + 3.

Step-by-step explanation:

c(3a) = 18a^2 - 12a + 3

Note: this is the simplified form of the expression.

If Hiba needs 40g of sugar to make 15 biscuits. The amount of flour she needs is 480g and the number of packs of butter will she have to buy is 3 pack of butter.

a. Amount of flour she needs

Amount of flour she needs =(3×40) × 60/15

Amount of flour she needs = 120 × 60/15

Amount of flour she needs = 480g

b.  Packs of butter will she have to buy

Packs of butter needed = [(2×40) × 60/15] /125g

Packs of butter needed = [80 × 60/15] /125g

Packs of butter needed = 320 /125g

Packs of butter needed = 2.56

Packs of butter needed = 3 packs (Approximately)

Therefore the amount of flour she needs is 480g and the number of packs of butter will she have to buy is 3 pack of butter.

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Step-by-step explanation:

since you don't show us f(x) here, I can only tell you in general :

when you are asked for something like f(2), it means that x = 2, and that you have to replace all "x" in the f(x) definition by "2". and then you take the calculator, if necessary, and calculate.

Answer: We will do (A) then you will be able to do most of them

Step-by-step explanation: For (A) first write it down

18x - 2y=0

Now we can explore many different combinations but I will give you something simple

18(1) - 2(9)=0  (note that two numbers beside each other means multiplication)

Now we can see this is now = 18 - 18 = 0

Therefore , the solution of the given problem of mean comes out to be

23.679 the isotopic mass of the least abundant isotope.

The arithmetic mean, often known as the average, of a dataset is the total of all values divided by the number of values (as opposed to the geometric mean). It is the most used often index of central tendency, sometimes known as the "mean." This result can be obtained by simply dividing the number of variables values in the dataset by the sum of all the values.

Here,

The abundant isotope has an isotopic mass of 123.39 u, compared to the most prevalent isotope's mass of 121.560 u.

22.567 u is the average atomic mass.

84.236% is the most prevalent isotope.

22.653 u is the isotope's mass.

Least prevalent isotope: 100 - 84.236% = 15.764%

Take into account that x is the mass of both the least common isotope.

The same element's atoms called abundant isotopes have different quantities of neutrons than other isotopes. These species always have the same number of protons and electrons. Although there is a change in the number of neutrons, the atomic number is unaffected. The weighted value of all the isotopes that an element naturally presents is its atomic mass.

Average atomic mass is equal to the sum of the natural abundances of the isotopes A and x divided by 100.

=> 22.653 = ( 22.567 * 84.236) + (x * 15.764 ) / 100

=>22.653 * 100 = 1900.953 + 15.764 x

=> x = 22.653 * 100 - 1900.953/ 15.764

=> 23.679

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The proof is given as follows:

The transitive property argues that "if two quantities are equal to the third quantity, then we may claim that all the quantities are equal to one other".

The term transitive refers to a transfer. If there are three quantities a, b, and c, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule; this property is known as the transitive property of equality.

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The equation of the line passing through the point (-4, 1), and having a slope of m = -3/2 is 2y = -3x - 10.

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

The equation of the line passing through the points (x1, y1), with a slope of m is given by the formula:

(y - y1) = m (x - x1)

Given that the point is (-4, 1) and the slope, m = -3/2.

Substituting the values we have:

(y - y1) = m (x - x1)

y - 1 = -3/2 (x - (-4))

2(y - 1) = -3(x+ 4)

2y - 2 = -3x - 12

2y = -3x - 10

Hence, the equation of the line passing through the point (-4, 1), and having a slope of m = -3/2 is 2y = -3x - 10.

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On solving the provided question, we cans ay that by unitary method, for 875 miles = car will take 0.04*875 = 35 gallons

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

by unitary method,

Sera drove 450 miles

car used 18 gallons of gas

for 1 mile, car take = 18/450 = 0.04gallons

for 875 miles = car will take 0.04*875 = 35 gallons

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D -3/2 is the right answer. In other words, the sum of their slopes is -1. So, if the green line has a slope of 2/3, the red line has a slope of -3/2.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope of a line is its steepness as it goes from LEFT to RIGHT. Slope is the ratio of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always constant (it never changes) regardless of whatever two locations on the line are chosen. The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m.

Here,

The correct answer is D -3/2 that is, the product of their slopes is -1. So, if the slope of the green line is 2/3, then the slope of the red line is -3/2.

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Answer:

No, because 234 / 36 is 6.5 which is what Chad makes hourly. 288 / 40 is 7.2 which is what Geo makes hourly so it is not proportional.

Answer:

see  below

Step-by-step explanation:

Chad earns $234 for 36 hours of work.  so 234/36 = 6.5/hr

Geo earns $288 for 40 hours of work. so 7.2/hr

No they are not because their hourly rates are different.  

The value of fractions after subtraction is,

⇒ - (y² - 10y - 12) / (y - 4) × 1 / (y + 2)

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

⇒ y/ (y + 2) is subtracted from 6 / (y - 4).

Now, We can subtract as;

⇒ 6 / (y - 4) - y / (y + 2)

⇒ 6 (y + 2) - y (y - 4) / (y - 4) (y + 2)

⇒ (6y + 12 - y² + 4y) / (y - 4) (y + 2)

⇒ (- y² + 10y + 12) / (y - 4) (y + 2)

⇒ - (y² - 10y - 12) / (y - 4) (y + 2)

⇒ - (y² - 10y - 12) / (y - 4) (y + 2)

⇒ - (y² - 10y - 12) / (y - 4) × 1 / (y + 2)

Thus, The value of fractions after subtraction is,

⇒ - (y² - 10y - 12) / (y - 4) × 1 / (y + 2)

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The two expressions are equivalent is equal to 2y+19.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

(y+10)+y+9

⇒ y+y+10+9

⇒2y+19

using addition we get this.

now, we have,

and 2 (y+7)+5

⇒2y +14+5

⇒2y+19

using  multiplication & then addition , we get, this.

Hence, the two expressions are equivalent is equal to 2y+19.

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15/4 or 3 3/4 or 3.75

5 * 1 3/4 = 35/4 = 8 3/4 = 8.75

hope this helps! :)

Answer:

11,209

Step-by-step explanation:

1 x 10,000 is 10,000, 1 x 1,000 is 1,000 100 x 200 is 200, 0 x 10 = 0, 9 x 1 = 9. 10,000 + 1,000 + 200 + 0 + 9 = 11209

The current asset is $10,150, the total long term asset is $13108, the total current liabilities is $985, the long term liabilities is $9982 and the total equity is $12273

The company has $10,150 in current assets, which are made up of $8,250 in cash, $1,225 in inventory, and $675 in accounts receivable.

The company has $985 in current liabilities, which are made up of $485 payable to suppliers and a $500 loan that must be repaid in the following six months.

The owner's equity is equal to the $12,000 initial investment plus the $1,291 in earnings retained less the $2,018 in long-term loan repayment plus the $1,000 set aside for long-term investment, for a total of $12,273.

The value of the company's assets (land, buildings, and equipment) plus the owner's equity, or $12,273 + $8,878 + $4,230, equals the net worth of the business, or $25,381.

a) The current assets of the company are:

$8,250 in cash

$1,225 in inventory

$675 in accounts receivable

The current assets total $10,150.

b) The long-term assets of the company are:

Land and building worth $8,878

Equipment worth $4,230

The total long-term assets of the company are $8,878 + $4,230 = $13,108.

c)The current liabilities of the company are:

$485 owed to suppliers

$500 loan to be paid off in the next six months

The total current liabilities of the company are $485 + $500 = $985.

d)The long-term liability of the company is the five-year loan of $12,000, of which $2,018 has been paid back, leaving a remaining balance of

= $12,000 - $2,018 = $9,982.

e) The total equity of Company X

= $12,000 (initial investment) + $1,291 (retained earnings) - $2,018 (repaid long-term loan) + $1,000 (long-term investment)

= $12,273.

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[tex]\displaystyle \lim_{x\to 16} ~~ \cfrac{4-\sqrt{x}}{16x-x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{4-\sqrt{x}}{16x-x^2}\implies \cfrac{4-\sqrt{x}}{x(16-x)}\implies \cfrac{4-\sqrt{x}}{x( ~~ 4^2-(\sqrt{x})^2 ~~ )} \\\\\\ \cfrac{4-\sqrt{x}}{x( ~~ [4-(\sqrt{x})][4+(\sqrt{x})] ~~ )}\implies \cfrac{1}{x( ~~ 4+\sqrt{x} ~~ )} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to 16} ~~ \cfrac{1}{x( ~~ 4+\sqrt{x} ~~ )}\implies \cfrac{1}{16( ~~ 4+\sqrt{16} ~~ )}\implies \cfrac{1}{16(4+4)}\implies \cfrac{1}{128}[/tex]

Answer: To find the limit as x approaches 16, we can substitute x = 16 into the expression:

lim (4-√X)/16X-X² = (4 - √16)/16 * 16 - 16^2 = (4 - 4)/16 * 16 - 256 = 0/256 - 256 = -256.

So the limit as x approaches 16 is -256.

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Both approaches -1.

The table for the number of steps Anne walked in x hours is:

Hours    Steps

1             700

2            1400

3            2100

Anne walked more than Elyse for different numbers of hours.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Anne function:

y = 700x

Now,

The table for the number of steps Anne walked in x hours.

Hours    Steps

1             700

2            1400

3            2100

Now,

Anne has walked more than Elyse for different numbers of hours.

Thus,

The table comparison is given above.

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The correct equation for the graph include the following: C. y = 2x/3 - 4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At point (0, -4), a linear equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (0 + 4)/(6 - 0)(x - 0)

y + 4 = 2x/3

y = 2x/3 - 4

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Answer:

(x - 1)² + (y - 1)² = 25

Step-by-step explanation:

the distance from the center of the circle to any point on the edge (or arc) of the circle is the radius of the circle.

per the distance formula (= Pythagoras for the right-angled triangle of the coordinate differences between the 2 points) we know

AB² = (xb - xa)² + (yb - ya)² = (5 - 1)² + (4 - 1)² =

= 4² + 3² = 16 + 9 = 25

AB = radius = 5

the standard form of a circle is

(x - h)² + (y - k)² = r²

(h, k) being the coordinates of the center of the circle, r being the radius.

(x - 1)² + (y - 1)² = 25

is the correct equation.

The exact value of θ can not be expressed in terms of elementary functions and is difficult to find without numerical methods.

To find the angle of intersection between two curves, we need to find the dot product of the two vectors that represent their tangent lines at the intersection point.

Let's find the first derivative of both r1(t) and r2(t) with respect to t:

r1'(t) = -sint i + cost j + k

r2'(t) = i + 2tj + 3t^2 k

The tangent lines at (1,0,0) are given by:

r1'(1) = -sin(1) i + cos(1) j + k

r2'(1) = i + 2j + 3k

The angle of intersection between these two lines is given by the dot product of the two vectors divided by the product of their magnitudes:

cos(θ) = (r1'(1) * r2'(1)) / (||r1'(1)|| * ||r2'(1)||)

= (-sin(1)i + cos(1)j + k) * (i + 2j + 3k) / (||-sin(1)i + cos(1)j + k|| * ||i + 2j + 3k||)

To find the angle of intersection, we can use the arccosine function:

θ = arccos(cos(θ))

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The solution to the equations are as follows:

1. X^2 + 6X + 3 = 0, the solution is (-3,-1).

2. 52726 - 6 = 52,720

3. 12 - 8 + (-5) = -1

4. X^2 + 8X + 20 = 0, the solution is (-5, -4).

5. x⁻¹+4x⁻²=0

X^2 + 6X + 3 = 0, can be solved by the quadratic formula: X = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 6, and c = 3.

X = (-6 ± √(6^2 - 4 * 1 * 3)) / 2 * 1

X = (-6 ± √(36 - 12)) / 2

X = (-6 ± √(24)) / 2

X = (-6 ± 2√6) / 2

X = (-3 ± √6), (-3 - √6)

52726 - 6 = 52720

12 - 8 + (-5) = -1

X^2 + 8X + 20 = 0, can be solved by the quadratic formula: X = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 8, and c = 20.

X = (-8 ± √(8^2 - 4 * 1 * 20)) / 2 * 1

X = (-8 ± √(64 - 80)) / 2

X = (-8 ± √(-16)) / 2

Since the square root of a negative number is not defined in real numbers, there are no real solutions to this equation.

x⁻¹ + 4x⁻² = 0

Dividing both sides by x⁻², we get x + 4 = 0

Subtracting 4 from both sides, we get x = -4.

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The complete question goes thus:

Solve:

1.X2 +6x +3=0

2.52726-6=0

3.12-8+-5:0

4.X(X+8)=-20

5.x⁻¹+4x⁻²=0

The simplified form of the expression is 2/3x-1+2(x-6)​ is 8x/3 -13.

Bracket, Of, Division, Multiplication, Addition, and Subtraction is referred to as BODMAS. A mathematical expression's order of execution is explained using the BODMAS. The acronym PEDMAS, which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction, is sometimes used to refer to the BODMAS.

The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to BODMAS rule. Any expression can only be solved correctly if the BODMAS rule or the PEDMAS rule are applied.

The given expression is: 2/3x-1+2(x-6)​

2/3x-1+2(x-6)​

2/3x - 1 + 2x - 12

2/3x - 1 + 6x/3 -12

8x/3 -13

Hence the simplified form of 2/3x-1+2(x-6)​ is 8x/3 -13.

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